In general, seismic prospection consists in emitting seismic waves into underground formations by means of one or more seismic sources, and in using sensors such as geophones or hydrophones to record seismic data corresponding to seismic waves that have been reflected on underground geological interfaces (also known as "reflectors"), and then in processing said data in order to extract useful information about the underground geology.
It is conventional for the seismic source(s) and for the pressure sensors to be disposed along a prospecting line (also known as a "prospecting section"), at regular intervals when performing "2D" seismic prospecting, and at the nodes of a regular grid when performing "3D" seismic prospecting.
In order to obtain a true image of underground geology, in particular in order to establish the depth positions of reflectors, it is appropriate to process the seismic data recorded at the surface by taking account of the velocity field of seismic wave propagation underground, and in particular by taking account of variations in propagation velocities laterally and as a function of depth.
The usual treatment of seismic data is known as "multi-offset migration" or as "prestack migration" and, in extremely simplified outline, it consists in assuming, a priori, a field of propagation velocities for seismic waves underground, and then in calculating for each source-sensor pair on the surface, fictional recordings that would have been obtained by means of fictional sources and sensors situated at greater or lesser depths on the path of the seismic waves emitted and received by each source-sensor pair. In practice, a large number of source-sensor pairs situated at adjacent abscissa intervals over the prospecting section are treated simultaneously and the calculated fictional recording at any given point takes account of the contribution from all of the seismic sources disposed on the surface.
The image of the underground formations is obtained by applying special space and time conditions known as "imaging conditions" to the set of fictional recordings, where the time condition corresponds to time zero, while the space condition corresponds to fictional sources and sensors that coincide at points having the same abscissa on the prospecting section and referred to as the "zero offset extrapolation point", and having respective depths known as the "extrapolation depths". When the space and time conditions are implemented at the same extrapolation points, such a point is said to be the "imaging point" and the corresponding extrapolation depth is said to be the "imaging depth".
When the velocity field used in the extrapolation corresponds to the real velocity field, then the imaging depth of an imaging point corresponds to the exact depth of the reflector, and otherwise, any error in the assumed velocity field gives rise to an error in the depth position of the imaging point relative to the real depth of the reflector.
In order to facilitate estimating the field of seismic wave propagation velocities underground, proposals were made in 1986, in particular in the articles "Prestack migration velocities from depth focusing analysis", 56th Annual International Meeting of the Society of Exploration Geophysicists, Expanded Abstracts 438-440, and "2D prestack depth migration in the (S-G-W) domain", 56th Annual International Meeting of the Society of Exploration Geophysicists, Expanded Extracts 327-330, to establish a focusing data volume while conserving the extrapolated data corresponding to a zero offset and to a time interval that is not reduced to zero. That time interval is then converted into a depth positioning error for the zero offset extrapolation points, thereby constituting a focusing panel at constant abscissa on the prospecting section. By concentrating on the energy maxima of said focusing panels using a technique known as "depth focusing analysis" and described in particular in the article "Depth focusing analysis": Practical Applications and Potential Pitfalls, 61th International Meeting of the Society of Exploration Geophysicists, Expanded Abstracts 1222-1225 and the bibliography mentioned in that article, it is possible to estimate a new velocity field which, by reiterating the above-mentioned extrapolation process, makes it possible to obtain an image of underground geology that is closer to reality.
Nevertheless, in known treatment methods, the above-mentioned time interval is converted into an error in depth positioning without taking account of lateral variations in the velocity field, nor of the slope of the reflectors.
It is then difficult to act accurately on the energy maxima of the focusing panels, such that any improvement in the estimate of the velocity field that results therefrom is small and does not always justify the cost of the computation performed.